Chain rule and side parameter

Part of the Lecture Notes in Mathematics book series (LNM, volume 1909)

The essential ingredient of Jorgensen's work in [40] is a detailed analysis of how the pattern of isometric hemispheres bounding the Ford domain change as one varies the group. This idea can be found in his preceding work [39] on the infinite cyclic Kleinian groups. (See the work [25] due to Drumm and Poritz for its detailed exposition and generalization.) In this chapter we first describe the “chain rule for isometric circles” (Lemma 4.1.2), which affords a foundation on the analysis, and then we introduce the key notion of Jorgensen's side parameter (Definition 4.2.9) and prove various of its properties.


Triangle Inequality Chain Rule Parallel Argument Elliptic Generator Parallel Translation 
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© Springer-Verlag Berlin Heidelberg 2007

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